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Smooth Surface Reconstruction using DooSabin Subdivision Surfaces
"... A new technique for the reconstruction of a smooth surface from a set of 3D data points is presented. The reconstructed surface is represented by an everywhere continuous C1subdivision surface which interpolates all the given data points. The new technique consists of two major steps. First, an eff ..."
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the vertices of the polyhedral approximation until a new control mesh M, whose DooSabin subdivision surface interpolates M, is reached. This iterative process converges for meshes of any size and any topology. Therefore the surface reconstruction process is welldefined. The new technique has the advantages
PARAMETRIZATION AND SHAPE RECONSTRUCTION TECHNIQUES FOR DOOSABIN SUBDIVISION SURFACES
, 2007
"... This thesis presents a new technique for the reconstruction of a smooth surface from a set of 3D data points. The reconstructed surface is represented by an everywhere 1 CÂ¹continuous subdivision surface which interpolates all the given data points. And the topological structure of the reconstructed ..."
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that, for any mesh M with any size and any topology, the iterative process is always convergent with DooSabin subdivision scheme. The new technique has the advantages of both a local method and a global method, and the surface reconstruction process can reproduce special features such as edges
Interpolation over arbitrary topology meshes using DooSabin surfaces
"... Interpolating an arbitrary topology mesh by a smooth surface plays an important role in geometric modeling and computer graphics. In this paper we present an efficient new algorithm for constructing a DooSabin subdivision surface that interpolates a given mesh. By introducing additional degrees of ..."
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Interpolating an arbitrary topology mesh by a smooth surface plays an important role in geometric modeling and computer graphics. In this paper we present an efficient new algorithm for constructing a DooSabin subdivision surface that interpolates a given mesh. By introducing additional degrees
Primitives for the manipulation of general subdivisions and the computations of Voronoi diagrams
 ACM Tmns. Graph
, 1985
"... The following problem is discussed: Given n points in the plane (the sites) and an arbitrary query point 4, find the site that is closest to q. This problem can be solved by constructing the Voronoi diagram of the given sites and then locating the query point in one of its regions. Two algorithms ar ..."
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Cited by 543 (11 self)
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The following problem is discussed: Given n points in the plane (the sites) and an arbitrary query point 4, find the site that is closest to q. This problem can be solved by constructing the Voronoi diagram of the given sites and then locating the query point in one of its regions. Two algorithms are given, one that constructs the Voronoi diagram in O(n log n) time, and another that inserts a new site in O(n) time. Both are based on the use of the Voronoi dual, or Delaunay triangulation, and are simple enough to be of practical value. The simplicity of both algorithms can be attributed to the separation of the geometrical and topological aspects of the problem and to the use of two simple but powerful primitives, a geometric predicate and an operator for manipulating the topology of the diagram. The topology is represented by a new data structure for generalized diagrams, that is, embeddings of graphs in twodimensional manifolds. This structure represents simultaneously an embedding, its dual, and its mirror image. Furthermore, just two operators are sufficient for building and modifying arbitrary diagrams.
Subdivision
, 2010
"... The Draft Environmental Impact Statement (DEIS) for the Marian Meadows proposal east of the community of Easton is attached. This DEIS addresses several alternatives for development of approximately one square mile of land, including the applicantâ€™s Planned Unit Development (PUD) proposal for up to ..."
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to 449 units as well as alternatives including a variety of lot sizes and configurations ranging from 147 lots to 449 units. The alternatives discussed, as well as the Elements of the Environment addressed were determined as a result of a public scoping process from April to October, 2007. The purpose
A Signal Processing Approach To Fair Surface Design
, 1995
"... In this paper we describe a new tool for interactive freeform fair surface design. By generalizing classical discrete Fourier analysis to twodimensional discrete surface signals  functions defined on polyhedral surfaces of arbitrary topology , we reduce the problem of surface smoothing, or fai ..."
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Cited by 668 (15 self)
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. With this algorithm, fairing very large surfaces, such as those obtained from volumetric medical data, becomes affordable. By combining this algorithm with surface subdivision methods we obtain a very effective fair surface design technique. We then extend the analysis, and modify the algorithm accordingly
Subdivision based Interpolation with Shape Control
"... An interpolation technique with the capability of local shape control for meshes of arbitrary topology is presented. The interpolation is a progressive process which iteratively updates the given mesh, through a twophase DooSabin subdivision scheme, until a control mesh whose limit surface interpo ..."
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An interpolation technique with the capability of local shape control for meshes of arbitrary topology is presented. The interpolation is a progressive process which iteratively updates the given mesh, through a twophase DooSabin subdivision scheme, until a control mesh whose limit surface
3 subdivision
 In Proceedings of ACM SIGGRAPH
, 2000
"... A new stationary subdivision scheme is presented which performs slower topological refinement than the usual dyadic split operation. The number of triangles increases in every step by a factor of 3 instead of 4. Applying the subdivision operator twice causes a uniform refinement with trisection of ..."
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Cited by 141 (4 self)
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. The smoothness of the limit surface is C2 everywhere except for the extraordinary points where it is C1. The convergence analysis of the scheme is presented based on a new general technique which also applies to the analysis of other subdivision schemes. The new splitting operation enables locally adaptive
Results 1  10
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119,854